Enigma 442a: Hark the herald angels sing
30 March 2018
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From New Scientist #1592, 24th December 1987 [link]
“Have a mince pie.”
“Thanks. How did the carol singing go this evening?”
“Very well indeed. There were 353 of us. We started from the village church at 6:00pm and arrived here at the hall some time ago. Have a look at this map here on the wall.
“We divided into groups and between us we covered every one of the 12 roads once. For each road, the group would enter at one end, sing the carols as they walked along the road, and leave at the other end. At each of the five junctions, all the groups due to arrive at that junction would come together and then re-divide before setting off again.”
“Did you sing many carols?”
“On each road, every member of the group would sing one verse as a solo. A verse takes one minute to sing.”
“Did people get cold waiting at the junctions for the other groups to join them?”
“No. That is the marvellous thing. We had divided into groups so that, at each junction, all the groups for that junction arrived at precisely the same time. Similarly, all the groups arrived at the hall at the same time.”
“You were very fortunate — a little miracle.”
“Don’t forget,” said the vicar who had been standing with us, “it is Christmas Eve.”
What time did the singers arrive at the hall and what was the total number of verses that they sang?